1. Field of the Invention
This invention relates to quantum computing and, in particular, to a control system for performing operations on a quantum qubit.
2. Description of Related Art
Research on what is now called quantum computing traces back to Richard Feynman, See, e.g., R. Feymnan, Int. J. Theor. Phys., 21, 467-488 (1982). Feynman noted that quantum systems are inherently difficult to simulate with classical (i.e., conventional, non-quantum) computers, but that this task could be accomplished by observing the evolution of another quantum system. In particular, solving a theory for the behavior of a quantum system commonly involves solving a differential equation related to the Hamiltonian of the quantum system. Observing the behavior of the quantum system provides information regarding the solutions to the equation.
Further efforts in quantum computing were initially concentrated on xe2x80x9csoftware developmentxe2x80x9d or building of the formal theory of quantum computing. Software development for quantum computing involves attempting to set the Hamiltonian of a quantum system to correspond to a problem requiring solution. Milestones in these efforts were the discoveries of the Shor and Grover algorithms. See, e.g., P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997); L. Grover, Proc. 28th STOC, 212-219 (1996); and A. Kitaev, LANL preprint quant-ph/9511026 (1995). In particular, the Shor algorithm permits a quantum computer to factorize large numbers efficiently. In this application, a quantum computer could render obsolete all existing xe2x80x9cpublic-keyxe2x80x9d encryption schemes. In another application, quantum computers (or even a smaller scale device such as a quantum repeater) could enable absolutely safe communication channels where a message cannot be intercepted without being destroyed in the process. See, e.g., H. J. Briegel, W. Dur, J. I. Cirac, P. Zoller, LANL preprint quant-ph/9803056 (1998).
Showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations of quantum computers. See, e.g., E. Knill, R. Laflamme, and W. Zurek, Science, 279, p. 342 (1998). One proposed application of a quantum computer is factoring of large numbers. In such an application, a quantum computer could render obsolete all existing encryption schemes that use the xe2x80x9cpublic keyxe2x80x9d method. In another application, quantum computers (or even a smaller scale device such as a quantum repeater) could enable absolutely safe communication channels where a message, in principle, cannot be intercepted without being destroyed in the process. See, e.g., H. J. Briegel et al., LANL preprint quant-ph/9803056 (1998).
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among the N qubits, allowing the states of the qubit system to evolve, and reading the qubits afterwards. A qubit is conventionally a system having two degenerate (of equal energy) quantum states, with a non-zero probability of the system being found in either state. Thus, N qubits can define an initial state that is a combination of 2N classical states. This entangled initial state will undergo an evolution, governed by the interactions which the qubits have both among themselves and with external influences. This evolution defines a calculation, in effect 2N simultaneous classical calculations, performed by the qubit system. Reading out the qubits after evolution is complete determines their states and thus the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses molecules having degenerate nuclear spin states, see N. Gershenfeld and I. Chuang, xe2x80x9cMethod and Apparatus for Quantum Information Processingxe2x80x9d, U.S. Pat. No. 5,917,322. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented a search algorithm, see, e.g., M. Mosca, R. H. Hansen, and J. A. Jones, xe2x80x9cImplementation of a quantum search algorithm on a quantum computer,xe2x80x9d Nature, 393:344-346, 1998 and the references therein, and a number ordering algorithm, see, e.g., Lieven M. K. Vandersypen, Matthias Steffen, Gregory Breyta, Costantino S. Yannoni, Richard Cleve and Isaac L. Chuang, xe2x80x9cExperimental realization of order-finding with a quantum computer,xe2x80x9d Los Alamos preprint quant-ph/0007017 (2000). The number ordering algorithm is related to the quantum fourier transform, an essential element of both Shor""s algorithm for factoring of a natural number and Grover""s Search Algorithm for searching unsorted databases. However, efforts to expand such systems to a commercially useful number of qubits face difficult challenges.
One method for determining the state of a radio-frequency superconducting quantum interference device (RF-SQUID) qubit (another type of phase qubit) involves rapid single flux quantum (RSFQ) circuitry See Roberto C. Rey-de-Castro, Mark F. Bocko, Andrea M. Herr, Cesar A. Mancini, Marc J. Feldman, xe2x80x9cDesign of an RSFQ Control Circuit to Observe MQC on an rf-SQUID,xe2x80x9d IEEE Trans. Appl. Supercond, 11, 1014 (March 2001). A timer controls the readout circuitry and triggers the entire process with a single input pulse, producing an output pulse only for one of the two possible final qubits states. The risk of this readout method lies in the inductive coupling with the environment causing decoherence or disturbance of the qubit during quantum evolution. The readout circuitry attempts to reduce decoherence by isolating the qubit with intermediate inductive loops. Although this may be effective, the overhead is large, and the overall scalability is limited.
One physical implementation of a phase qubit involves a micrometer-sized superconducting loop with 3 or 4 Josephson junctions. See J. E. Mooij, T. P. Orlando, L. Levitov, Lin Tian, Caspar H. van der Wal, and Seth Lloyd, xe2x80x9cJosephson Persistent-Current Qubitxe2x80x9d, Science 1999 Aug. 13; 285: 1036-1039. The energy levels of this system correspond to differing amounts of magnetic flux threading the superconducting loop. Application of a static magnetic field normal to the loop may bring two of these levels (or basis states) into degeneracy. Typically, external AC electromagnetic fields are applied, to enable tunneling between non-degenerate states.
Further, currently known methods for entangling qubits also are susceptible to loss of coherence. Entanglement of quantum states of qubits can be an important step in the application of quantum algorithms. See for example, P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997). Current methods for entangling phase qubits require the interaction of the flux in each of the qubits, see Yuriy Makhlin, Gerd Schon, Alexandre Shnirman, xe2x80x9cQuantum state engineering with Josephson-junction devices,xe2x80x9d LANL preprint, cond-mat/0011269 (November 2000). This form of entanglement is sensitive to the qubit coupling with surrounding fields which cause decoherence and loss of information.
As discussed above, currently proposed methods for readout, initialization, and entanglement of a qubit involve detection or manipulation of magnetic fields at the location of the qubit, which make these methods susceptible to decoherence and limits the overall scalability of the resulting quantum computing device. Thus, there is a need for an efficient implementation and method that minimizes decoherence and other sources of noise and maximizes scalability.
In accordance with the present invention, a quantum computing system includes a control system which utilizes currents and voltages for performing operations on qubits. The operations performed on the qubits can include reading the state of the qubit, initializing the state of the qubit, and entangling the state of the qubit with the states of other qubits in the quantum computing system. In some embodiments, the qubits include permanent readout superconducting qubits (PRSQs). Embodiments of the invention, however, can include any phase qubit.
In some embodiments of the invention, the control system is capable of grounding a phase qubit. Grounding the phase qubit freezes the quantum tunneling between the two degenerate states. When the qubit is grounded, electrons freely move between the qubit and the ground, thus collapsing the wavefunction of the supercurrent into one of the ground states xc2x1"PHgr"0, having a definite magnetic moment. Thus, while the grounding connection is open, the qubit remains in that state to be read. In some embodiments, the control includes a single electron transistor or parity key that couples the qubit to ground. By modulating the voltage on the single electron transistor (SET), the circuit can be opened and closed, and furthermore, the SET can be tuned for a single electron or a Cooper pair (pair of electrons) depending on the particular qubit.
In some embodiments of the invention, the control system can apply current through the qubit in order to read the quantum state of the qubit. Degeneracy in the ground states of the qubit means that if a current is driven through the qubit, the flux will behave differently depending on the quantum state of the qubit when grounded (ie, xc2x1"PHgr"0). Since the voltage across the qubit is proportional to the derivative of the quantum flux in the qubit with respect to time, which is dependent on the quantum state of the qubit, the resulting voltage across the qubit will also be different depending on the state of the qubit. Therefore, the quantum state of the qubit can be read by grounding the qubit and driving a current through the qubit while measuring the resulting voltage across the qubit. The measured voltage across the qubit indicates one of the states of the qubit.
In some embodiments of the invention, the control system can initialize the qubit to occupy one of its basis states. The bistability of the ground state in the qubit occurs when the current through the qubit is zero, where the classical basis states of the qubit are xc2x1"PHgr"0. By driving current across the qubit in a particular direction, a first state can be selected, and conversely, by driving a current across the qubit in the opposite direction a second state can be selected. Therefore, a control system according to the present invention can initialize a first state by driving current across the qubit in a first direction and can initialize a second state by driving current across the qubit in a second direction opposite from the first direction.
Further, in some embodiments a control system according to the present invention can control entanglements between quantum states of qubits in the quantum computing system. Once a qubit has been initialized and released from the fixed state, it becomes free to evolve quantum mechanically. The evolving wavefunction stores the quantum information of the qubit as a superposition of states. In order to entangle qubits, the evolving wavefunctions are allowed to overlap.
In some embodiments of the invention, a qubit system can consist of a 2-dimensional grid of individual phase qubits. For example, a grid can have N rows and M columns of qubits, wherein each index can have a phase qubit. Each row of the grid can have at least one line for application of a current, and at least one line for grounding operations. Similarly, each column of the grid can have at least two lines for application of a voltage. In a qubit system, each qubit in a column could have a qubit switch, such that application of a voltage to the switch could effectively close the switch, thus allowing current to pass when the qubit is grounded. Each qubit could have a grounding switch connecting the qubit to a grounding mechanism, such that a voltage applied to the switch will close the switch and ground the qubit. Each row in the qubit system could have a current line such that application of a current (or supercurrent) to the line, will flow through the qubit to ground when the qubit switch and grounding switch are closed. Furthermore, a mechanism for measuring the potential drop can be placed between each respective current line and ground line for measuring the potential drop between the two. Some embodiments of the invention can have the described current, voltage, and ground lines reversed by column and row respectively, or could otherwise have some combination of current and voltage lines for a given row or column.
These and other embodiments are further described below with respect to the following figures.